A method for establishing an equivalent calculation model of a rail transmission line, a terminal and a medium

Abstract

The application relates to the technical field of rail transit lightning protection and electrical safety analysis, and discloses a method for establishing an equivalent calculation model of a steel rail transmission line, a terminal and a medium. The method is applied to lightning transient analysis of a non-standard I-shaped structure steel rail. First, two layers of cylindrical current layers are arranged outside a steel rail conductor; then, impedance parameters of a system composed of the inner cylindrical current layer and the steel rail, impedance parameters of a system composed of the outer cylindrical current layer and the ground and mutual impedance parameters of the steel rail are calculated; the influence of skin effect and magnetic saturation effect on the impedance parameters of the steel rail is analyzed by using finite element software, and a final steel rail frequency domain impedance parameter matrix used for modeling is obtained according to the analysis result; and finally, a time domain transmission line equation containing frequency variable parameters is established based on the steel rail frequency domain impedance parameter matrix. The application can obtain the frequency domain characteristic parameters of the conductor impedance of a steel rail section, analyze the influence law of magnetic saturation nonlinearity on the internal impedance parameters of the steel rail, and establish a lightning transient response calculation model of the steel rail.

Description

Technical Field

[0001] This invention relates to the field of lightning protection and electrical safety analysis technology for rail transit, specifically a method for establishing an equivalent calculation model of a rail transmission line, a terminal, and a medium. Background Technology

[0002] The track circuit system is a non-insulated frequency-shift automatic block system that uses rails as transmission conductors. Outdoor equipment such as tuning and matching units and hollow coils are distributed along the rails and directly connected to them. When the contact network is struck by lightning, transient overvoltages occur on the rails through spatial electromagnetic coupling and ground potential conduction. These transient overvoltages propagate along the rails and are further conducted to the track circuit system, causing damage to its equipment. Therefore, when calculating and analyzing the lightning overvoltage in the track circuit system, the propagation and distribution of overvoltage on the rails must be considered, requiring accurate modeling of the rails. The lateral dimension of the rail transmission system is smaller than the minimum characteristic wavelength of the lightning overvoltage, while its longitudinal dimension is much larger than the lateral dimension. While a transmission line model can be used for equivalence, the irregular I-shaped structure of the rail cross-section, the magnetic saturation of the rail material, and the non-uniform current distribution caused by the skin effect pose challenges to extracting the impedance parameters of the transmission line.

[0003] Currently, methods for calculating and analyzing the impedance frequency-varying characteristics of conductors with circular or tubular cross-sections, such as overhead transmission lines and cables, due to the skin effect and proximity effect are relatively mature. However, the acquisition of transient characteristics of rail lightning strikes mainly relies on experimental testing. Models and experiments are generally based on a single frequency of 50Hz, while lightning current energy is mainly concentrated in the 0~1MHz frequency range. Within this frequency band, the conductor impedance will exhibit frequency-varying characteristics due to the skin effect, and the ground return impedance will exhibit characteristics approaching the ground surface due to the conductor proximity effect and skin effect. Therefore, when traditional methods for acquiring transient characteristics of rail lightning strikes are used to establish equivalent models of rail transmission lines, the frequency-varying characteristics of the rail are ignored, and the influence of magnetic saturation characteristics and skin effect is not considered, resulting in a lack of accuracy. Summary of the Invention

[0004] To address the technical problems existing in the prior art, this invention provides a method, terminal, and medium for establishing an equivalent calculation model of a rail transmission line. This method can obtain the frequency domain characteristic parameters of the non-standard I-shaped cross-section conductor impedance of the rail, analyze the influence of magnetic saturation nonlinearity on the internal impedance parameters of the rail, and then establish a calculation model for the transient response of the rail to lightning strikes.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] This invention discloses a method for establishing an equivalent calculation model of a rail transmission line, applied to the transient analysis of lightning strikes on non-standard I-beam rails. The method includes the following steps:

[0007] S1. Two virtual cylindrical current layers are set outside the rail conductor to wrap the rail, thereby simplifying the lossy semi-infinite space electromagnetic field where the rail is located into a system composed of the inner cylindrical current layer and the rail, and a system composed of the outer cylindrical current layer and the ground.

[0008] S2. Calculate the impedance parameters of the system composed of the inner cylindrical surface current layer and the rail, the impedance parameters of the system composed of the outer cylindrical surface current layer and the earth, and the mutual impedance parameters of the rail respectively.

[0009] S3. The influence of skin effect and magnetic saturation effect on rail impedance parameters is analyzed using finite element software. Based on the analysis results, the final rail frequency domain impedance parameter matrix used for modeling is obtained.

[0010] S4. Based on the rail frequency domain impedance parameter matrix, establish the time domain transmission line equation containing frequency-varying parameters.

[0011] As a further improvement to the above scheme, in step S1, the current amplitude applied to the two cylindrical surface current layers is equal to the rail current, and the current directions of the inner and outer cylindrical surfaces are opposite, while the current direction of the outer cylindrical surface is the same as that of the rail current; the difference in the cylindrical radius of the two cylindrical surface current layers is within a set threshold, and the current density is uniformly distributed on the cylindrical surface, so that the electromagnetic fields generated by the two cylindrical surface current layers cancel each other out.

[0012] As a further improvement to the above scheme, step S2, calculating the impedance parameters of the system composed of the inner cylindrical surface current layer and the rail, specifically includes:

[0013] Obtaining the rail's self-impedance parameters: The electromagnetic field of the system consisting of the inner cylindrical surface current layer and the rail is solved using finite element software. Based on the power loss per unit length and the energy stored in the inductance, the resistance and inductance per unit length are calculated as follows:

[0014] ;

[0015] In the formula, Represents the resistance per unit length of the rail; This indicates the power loss per unit length of rail. Indicates the peak value of the excitation current; Represents the spatial current density distribution; Indicates the inductance per unit length of the rail; This represents the magnetic energy stored per unit length of rail. Indicates the distribution of magnetic flux density; Indicates the distribution of magnetic field strength; This indicates the cross-section of the rail. Represents an area element; Indicates the electrical conductivity of the rail;

[0016] Obtaining the internal impedance parameters of the rail: Finite element method (FEM) software is used to calculate the power loss and stored magnetic field energy of the rail within the current layer of the inner cylindrical surface of a set radius, obtaining the resistance and inductance at different frequencies. The frequency-varying internal impedance parameters are then calculated using the following formula:

[0017] ;

[0018] In the formula, This represents the distributed impedance parameter of the rail. This represents the internal resistance of the rail that varies with the frequency of the excitation current. Represents the imaginary unit. Indicates angular frequency; Indicates the self-inductance of the rail; This represents the external equivalent inductance.

[0019] As a further improvement to the above scheme, step S2, calculating the impedance parameters of the system consisting of the outer cylindrical surface current layer and the ground, specifically includes:

[0020] The external impedance per unit length of rail is calculated using the following formula. :

[0021] ;

[0022] In the formula, Represents the imaginary unit. Indicates angular frequency; Indicates the permeability of free space; Indicates the height of the rail above the ground; Indicates the radius of the current layer on the outer cylindrical surface; This represents the complex propagation constant of the earth.

[0023] As a further improvement to the above scheme, the complex propagation constant of the earth... The calculation formula is:

[0024] ;

[0025] In the formula, It represents the electrical conductivity of the earth; This represents the dielectric constant of the earth.

[0026] As a further improvement to the above scheme, in step S2, the rail mutual impedance parameters are calculated using the generalized integral form of Carson ground impedance:

[0027] ;

[0028] In the formula, Indicates frequency as At that time, the steel rail and rails mutual impedance between Represents the imaginary unit. Indicates angular frequency; Indicates the permeability of free space; It is a natural constant; and These represent two adjacent rails. and Distance to the ground, ; Indicates the horizontal distance between two rails; Represents the integral variable; It represents the electrical conductivity of the earth.

[0029] As a further improvement to the above scheme, in step S3, the influence of magnetic saturation effect on the rail's self-impedance parameters is ignored; under the skin effect, the amplitude of the magnetic field and the current density inside the rail vary with the distance from the conductor surface. y The increase exhibits exponential decay, as shown in the following formula:

[0030] ;

[0031] In the formula, y Indicates the depth from the surface of the conductor into the interior; Indicates depth Complex current density at the location, Represents the complex current density on the surface of a conductor; It is a natural constant; Indicates skin depth. Represents the imaginary unit. and These represent the decay constant and the phase constant, respectively. For skin depth The magnetic field amplitude decays to the level of the conductor surface. ; express Magnetic field strength at depth; The complex magnetic field strength at the surface of a conductor; skin depth The calculation formula is:

[0032] ;

[0033] In the formula, and These represent the electrical conductivity and magnetic permeability of the material, respectively. This indicates the frequency at which the current is applied.

[0034] As a further improvement to the above scheme, in step S4, the expression formula of the time-domain transmission line equation containing frequency-varying parameters is as follows:

[0035] ;

[0036] In the formula, Represents partial derivatives; Represents a point in the transmission line x In time t The voltage; This represents the inductance matrix per unit length of a multi-conductor transmission line. Represents a point in the transmission line In time The current; Representing fractional impedance Z ( s freq The number of terms in a function fraction; and They represent Z ( s freq Residues and poles of partially fractional expressions; The symbol for convolution; This represents the capacitance matrix per unit length of a multi-conductor transmission line.

[0037] The present invention also discloses a computer terminal, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the method for establishing an equivalent calculation model of a rail transmission line as described above.

[0038] The present invention also discloses a computer-readable storage medium having a computer program stored thereon, wherein when the program is executed by a processor, it implements the steps of the method for establishing an equivalent calculation model of a rail transmission line as described above.

[0039] Compared with the prior art, the beneficial effects of the present invention are:

[0040] 1. This invention addresses the characteristics of non-standard I-shaped rail structures by constructing two cylindrical surfaces with equal magnitudes and opposite directions of current enveloping the rail. It transforms the calculation of rail impedance parameters into two sub-problems: the impedance parameters between the rail and the inner cylindrical surface, and the impedance parameters between the outer cylindrical surface and the earth. This effectively reduces the difficulty of calculating the impedance parameters per unit length of the rail and solves the problem of needing to solve the open-domain calculation of a semi-infinite lossy spatial electromagnetic field for calculating the rail impedance per unit length.

[0041] 2. Based on the calculation and analysis of the effects of skin effect and magnetic saturation effect on the rail internal impedance parameters, this invention proposes that the magnetic saturation effect can be ignored when extracting rail internal impedance parameters within the frequency range of lightning transient overvoltages. The established transmission line equivalent model suitable for rail lightning transient analysis, by calculating the rail impedance parameters during lightning transients, can more accurately predict and analyze the impact of lightning overvoltages on the track system, especially under high-frequency current conditions. This provides a basis for lightning protection design of rail transit systems and improves the safety of railway systems. Attached Figure Description

[0042] Figure 1 This is a flowchart of the method for establishing the equivalent calculation model of the rail transmission line in Embodiment 1 of the present invention.

[0043] Figure 2 This is a schematic diagram of the arrangement of the rail and the double-layer cylindrical current layer in Embodiment 1 of the present invention.

[0044] Figure 3 This is a schematic diagram of the test setup for the transient impact response test of the rail in Embodiment 1 of the present invention.

[0045] Figure 4 This is a schematic diagram of the test wiring for the transient impact response test of the rail in Embodiment 1 of the present invention.

[0046] Figure 5 This is a voltage waveform diagram at the connection point of the impulse source and the matching resistor in Embodiment 1 of the present invention.

[0047] Figure 6 This is a waveform diagram of the injection point current I in Embodiment 1 of the present invention.

[0048] Figure 7 The voltage V between rail A and ground in Embodiment 1 of this invention A Waveform diagram.

[0049] Figure 8 The induced voltage V between rail B and ground in Embodiment 1 of this invention B Waveform diagram.

[0050] Figure 9 This is a schematic diagram of the structure of the computer terminal in Embodiment 2 of the present invention. Detailed Implementation

[0051] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0052] Example 1

[0053] Please see Figure 1 This embodiment provides a method for establishing an equivalent calculation model of a rail transmission line, which is applied to the transient analysis of lightning strikes on non-standard I-shaped rails. The method includes the following steps, namely S1 to S4.

[0054] Step S1: As Figure 2 As shown, two virtual cylindrical current layers are set outside the rail conductor to wrap around the rail. and Their radii are respectively r int and r ext Apply current amplitude I int , I ext With rail current I track If the currents in the two cylinders are equal, and their directions are opposite, then the current in the outermost cylinder is equal. I ext With rail current I track The same, as long as the radius r int and r ext If the two cylindrical current layers are sufficiently close (within the set threshold radius difference) and the current density is uniformly distributed on the cylindrical surface, the electromagnetic fields generated by the two cylindrical current layers cancel each other out everywhere. Therefore, the introduction of the virtual cylindrical current layer will not change the electromagnetic field distribution in the space where the rail is located. Thus, the lossy semi-infinite spatial electromagnetic field where the rail is located is simplified to a system composed of the inner cylindrical current layer and the rail, and a system composed of the outer cylindrical current layer and the ground.

[0055] Step S2: Calculate the impedance parameters of the system composed of the inner cylindrical current layer and the rail, the impedance parameters of the system composed of the outer cylindrical current layer and the earth, and the mutual impedance parameters of the rail.

[0056] In step S2, the calculation of the impedance parameters of the system consisting of the inner cylindrical surface current layer and the rail specifically includes:

[0057] Obtain the rail self-impedance parameters:

[0058] The electromagnetic field of the system consisting of the rail and the inner current layer can be calculated using finite element method (FEM) software. Since the rail impedance parameter calculation proposed in this invention is intended for the analysis of lightning transient processes, the hysteresis loss caused by repeated magnetization during the transient process can be ignored. The initial magnetization curve of the rail material is used to characterize its nonlinearity. Changes in the internal magnetic field of the rail induce eddy currents circulating within it. The direction of these eddy currents is perpendicular to the direction of the magnetic field. The governing equations for the vector magnetic potential and electrical potential inside the rail are shown below:

[0059] ;

[0060] In the formula, Represents the gradient operator, Represents the magnetic vector potential. and These represent the electrical conductivity and magnetic permeability of the rail, respectively. j The imaginary unit, Angular frequency, Where is the dielectric constant. For electric potential, I t Indicates the total current. S This represents the cross-section of a rail, with a uniform electromagnetic field distribution along the rail direction. The problem is a typical two-dimensional problem, so a rectangular coordinate system is established, and the magnetic induction intensity vector... B Only xy The electric field intensity vector has a value on a plane. E Only z The axial component ensures that the potential at any point on any cross-section is constant; this condition is satisfied in air. Based on the power loss per unit length and the energy stored in the inductor, the formulas for calculating the resistance and inductance per unit length are as follows:

[0061] ;

[0062] In the formula, Represents the resistance per unit length of the rail; This indicates the power loss per unit length of rail. Indicates the peak value of the excitation current; Represents the spatial current density distribution; Indicates the inductance per unit length of the rail; This represents the magnetic energy stored per unit length of rail. Indicates the distribution of magnetic flux density; Indicates the distribution of magnetic field strength; This indicates the cross-section of the rail. Represents an area element; This indicates the electrical conductivity of the rail.

[0063] Obtaining the internal impedance parameters of the rail: A virtual cylindrical surface with a radius of 18cm is set outside the rail to calculate the inductance. Finite element software is used to calculate the power loss and stored magnetic field energy inside the 18cm radius circle, and the resistance at different frequencies is obtained. and inductor Based on the characteristic that the external inductance in air does not change significantly with increasing frequency, the inductance value at high frequencies is approximately equal to the external inductance. L ext Its frequency-varying internal impedance parameters can be calculated using the following formula:

[0064] ;

[0065] In the formula, This represents the distributed impedance parameter of the rail. This represents the internal resistance of the rail that varies with the frequency of the excitation current. Represents the imaginary unit. Indicates angular frequency; Indicates the self-inductance of the rail; This represents the external equivalent inductance.

[0066] In step S2, calculating the impedance parameters of the system consisting of the outer cylindrical current layer and the ground specifically includes:

[0067] The impedance of the outer cylindrical surface includes the self-inductance of the outer cylindrical surface and the ground return impedance, which can be directly calculated using the following formula:

[0068] ;

[0069] In the formula, This represents the external resistance per unit length of rail. Indicates the permeability of free space; Indicates the height of the rail above the ground; Indicates the radius of the current layer on the outer cylindrical surface; This represents the complex propagation constant of the earth. The calculation formula is:

[0070] ;

[0071] In the formula, It represents the electrical conductivity of the earth; This represents the dielectric constant of the earth.

[0072] Calculation of rail mutual impedance parameters:

[0073] Rails are typically laid in pairs side-by-side to support train operation. Adjacent rails experience interference due to spatial coupling. Considering the influence of the ground, the mutual impedance between rails can be expressed by the generalized integral of Carson's ground impedance as follows:

[0074] ;

[0075] In the formula, Indicates frequency as At that time, the steel rail and rails mutual impedance between Indicates angular frequency; Indicates the permeability of free space; It is a natural constant; and These represent two adjacent rails. and Distance to the ground, ; Indicates the horizontal distance between two rails; Represents the integral variable; It represents the electrical conductivity of the earth.

[0076] Step S3: Use finite element software to analyze the effects of skin effect and magnetic saturation effect on rail impedance parameters, and obtain the final rail frequency domain impedance parameter matrix for modeling based on the analysis results.

[0077] First, the influence of magnetic saturation characteristics on the rail's self-impedance parameters is calculated and analyzed:

[0078] Based on the calculated rate of change of rail self-impedance, the magnetic saturation characteristics of the rail material have a relatively small impact on self-impedance in both low-frequency and high-frequency ranges, and the rate of change of self-impedance decreases with increasing current. The influence of rail material magnetic saturation on self-impedance parameters is more significant in the 1–400 Hz range, with the rate of change of self-impedance increasing relatively with increasing current, reaching its maximum around 10 Hz. The frequency components of lightning overvoltage show a gradual decreasing trend from low to high frequencies, with the low-frequency components accounting for the largest proportion. Since the frequency band where rail magnetic saturation characteristics are significant is limited to the 1–400 Hz range, the impact of rail magnetic saturation characteristics on lightning transient processes is limited. This indicates that the influence of magnetic saturation on rail self-impedance can be ignored for the calculation and analysis of rail lightning transient processes.

[0079] Calculation and analysis of the effects of skin effect and magnetic saturation effect on rail internal impedance parameters:

[0080] The internal impedance of a rail pair is mainly affected by the skin effect and magnetic saturation effect. The skin effect primarily occurs when a changing electromagnetic field generates eddy currents within the conductor, which cancel out the original electric field. In an isotropic homogeneous medium, the amplitude of the internal magnetic field and the current density increase with distance from the conductor surface. y The increase exhibits exponential decay, as shown in the following formula:

[0081] ;

[0082] In the formula, y Indicates the depth from the surface of the conductor into the interior; Indicates depth Complex current density at the location, Represents the complex current density on the surface of a conductor; It is a natural constant; Indicates skin depth. Represents the imaginary unit. and These represent the decay constant and the phase constant, respectively. For skin depth The magnetic field amplitude decays to the level of the conductor surface. ; express Magnetic field strength at depth; The complex magnetic field strength at the surface of a conductor; skin depth The calculation formula is:

[0083] ;

[0084] In the formula, and These represent the electrical conductivity and magnetic permeability of the material, respectively. This indicates the frequency at which the current is applied.

[0085] Since steel rails are typical ferromagnetic materials, transient lightning strike calculations can neglect hysteresis losses caused by repeated magnetization, considering only the effect of nonlinear changes in permeability caused by the initial magnetization curve. The internal magnetic field distribution of the steel rail can be calculated using the following formula:

[0086] ;

[0087] ;

[0088] In the formula, express x Directional magnetic field strength, express x Directional magnetic flux density Indicates the electrical conductivity of a material. Indicates incremental permeability. and These represent the macroscopic magnetic induction intensity and magnetic field intensity of the material, respectively.

[0089] To analyze the influence of excitation current frequency and amplitude on the rail, finite element method (FEM) software was used to calculate the rail cross-sectional current density distribution when the excitation current frequencies were 1Hz, 10Hz, 50Hz, 1000Hz, and 1MHz, and the amplitudes were 100A and 1000A, respectively. It was found that when the excitation source frequency was 1Hz, the rail current distribution showed a trend of increasing current density closer to the rail surface, indicating that the current skin effect was already present. Furthermore, as the excitation current frequency and amplitude increased, the maximum percentage difference in current density increased, indicating that the rail current density distribution became more uneven with increasing excitation current frequency and amplitude.

[0090] Because the current density distribution in the rail becomes more uneven with increasing excitation current frequency and amplitude, the rail internal resistance is determined based on the excitation current frequency of 0.03Hz~1MHz and the current amplitude of 100A~1000A. R int and internal inductance L int The calculation results show that the internal resistance of the rail is R int The internal resistance increases significantly with increasing frequency and also increases with increasing excitation current amplitude. At low frequencies, the internal resistance is approximately equal to the DC resistance, and the value is relatively small. As the frequency increases, the skin effect becomes more pronounced, and the internal resistance increases rapidly. Simultaneously, the internal resistance increases with increasing excitation current amplitude, with the most significant increase occurring when the current increases from 100A to 200A. Due to the magnetic saturation characteristics of the rail material, a significant saturation phenomenon occurs in the internal resistance when the current increases above 800A. It can be considered that when the current amplitude increases above 1000A, the internal resistance tends to reach its saturation value. (Rail internal inductance value) L int The internal inductance decreases with increasing frequency, showing a significant decrease around 1Hz. The most rapid decrease occurs in the range of 1Hz to 1kHz, and the internal inductance decreases further above 10kHz. L int Gradually approaching 0; as the amplitude of the excitation current increases, the internal inductance value L int As the current increases from 100A to 200A, the increase in internal inductance is most significant. Similarly, due to the magnetic saturation characteristics of the rail material, when the current increases to over 800A, the internal inductance tends to reach saturation.

[0091] Step S4: Based on the rail frequency domain impedance parameter matrix, establish the time domain transmission line equation containing frequency-varying parameters.

[0092] The frequency domain impedance parameter matrix of the rail is obtained through calculation and analysis in steps S2 and S3. Z ( s The rational function obtained by vector matching and fitting the impedance matrix can be written in the following partial fractional form:

[0093] ;

[0094] In the formula, c k , d k These are the residues and poles of the partial fractional expression, respectively. N z Representing fractional impedance Z ( s The number of terms in a function fraction; For complex frequency domain variables; This is the inductance per unit length of the rail.

[0095] In the parameters of a multi-conductor transmission line for rails, the ground admittance and cable-to-ground conductance can be ignored. Capacitance is a weakly frequency-dependent parameter. The admittance parameter matrix can be written in the form shown below:

[0096] ;

[0097] High-speed railways mostly adopt a double-track system with four rails laid in parallel. The equation for the multi-conductor transmission line in the complex frequency domain of the rails is shown below:

[0098] ;

[0099] In the formula, and For voltage and current column vectors, Z ( s )and Y ( s ) are the rational function expressions for the impedance and admittance parameters per unit length of a multi-conductor transmission line composed of rails.

[0100] Based on the Laplace transform, the expression for the time-domain transmission line equation containing frequency-varying parameters can be obtained as follows:

[0101] ;

[0102] In the formula, Represents partial derivatives; Represents a point in the transmission line x Voltage at a point over time t Changes; This represents the inductance matrix per unit length of a multi-conductor transmission line. Represents a point in the transmission line Current at point with time Changes; Representing fractional impedance Z ( s freq The number of terms in a function fraction; and They represent Z ( s freq Residues and poles of partially fractional expressions; The symbol for convolution; This represents the capacitance matrix per unit length of a multi-conductor transmission line.

[0103] To verify the effectiveness of this invention, a transient response test of the rail was conducted. The test setup was as follows: Figure 3As shown, the effective length of the rail under test is 33m. There is no overhead contact line or support above the rail. The rail is a 60kg / m rail widely used in my country's high-speed passenger railway lines. The insulation pads between the rail and the concrete sleepers have good performance. The impulse current source is connected to the rail through a matching resistor. When the grounding lead distance is greater than 80m, the grounding electrode of the impulse power source can be approximately considered to have a return current at near infinity, and its influence on the rail potential measurement is negligible. The rail potential measurement uses an oscilloscope attenuation probe, and the current acquisition uses a Pearson coil.

[0104] The test connection point layout is as follows Figure 4 As shown, the test power supply is connected to the first section of the rail through a matching resistor. A At rail end point 1, the return electrode of the impact power supply is located 80m away, and the injected current... I 1 On the rails A Voltage at measuring point 3 V 3 and rails B Voltage at measuring point 4 V 4 Recording was performed using an oscilloscope on the rails. A Impact self-impedance Z AA and rails A and B mutual impedance Z AB This can be calculated from waveform data. By changing the rail end connection method, and placing the rail end in three states—open circuit, short circuit, and terminating with a 60Ω resistor—the aforementioned impact test was performed for each. Based on the waveform reflection and refraction characteristics under different rail end states, the time it takes for the transient voltage wave to travel from the beginning of the rail, be reflected back to the beginning, and then be obtained. t If the length of the rail is known, the propagation speed of the transient waveform in the rail can be calculated.

[0105] The test results are as follows Figures 5 to 8 As shown, with the rail end open-circuited, the voltage waveform at the point where the impact source is connected to the matching resistor is as follows: Figure 5 As shown, the rising edge of the waveform is approximately 0.4. . Figure 6 The figure shows the injection point current. I Corresponding to the rails A The injected current wave at time t is measured under three conditions: open circuit, short circuit, and series impedance of 60Ω to ground. t d-I ≈0.77 They gradually separated over time. Figure 7 Rails for injecting current A Near-source rail voltage waveform, the curves in the figure correspond to the rails respectively. AThe voltage waveform at time t is as follows: open circuit, short circuit, and 60Ω series impedance at the terminal to ground. t d-U ≈0.77 As the rails gradually separate, according to the wave process principle, when a rail is short-circuited to ground, the voltage waveform undergoes negative total reflection while the current waveform undergoes positive total reflection. The voltage at the end of the rail drops to 0, while the current rises to twice its normal value, gradually increasing towards the beginning. Therefore, the time... t d-I , t d-U The reflected waveform from the rear end reaches the beginning of the rail, and the effective length of the rail during the test is... l rail The wave length is 32.71m, and the wave velocity in the rail is... v =2 l rail / t d-U ≈85m / Compared to overhead transmission lines or contact networks... Figure 6 and Figure 7 The 60Ω increase in the rail end relative to the ground did not achieve a complete match; both the current and voltage waveforms exhibited significant oscillations. t < t d-U Rails within the range A The reflected wave from the near-source end has not yet arrived; the rail's self-impedance equals the voltage divided by the injection point current amplitude, i.e. Z 11 = Z 22 =112Ω. In Figure 7 and Figure 8 In t < t d-U Rails within the range B The reflected wave from the near-source end has not yet arrived; the rail mutual impedance is equal to the induced rail voltage divided by the injection point current amplitude. Z 12 = Z 21 =103Ω.

[0106] Based on the field test conditions, a calculation model of a 33m long rail transmission line was established to calculate the rail-to-ground voltage waveform near the excitation source. The test measurement results and the model calculation results were compared. The rail-to-ground impulse voltage waves were measured under three conditions: open circuit, 60Ω, and short circuit. The test results were basically consistent with the model calculation results, and the amplitude deviation was less than 5%.

[0107] Example 2

[0108] This embodiment provides a computer terminal, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the method for establishing an equivalent calculation model of a rail transmission line as described in Embodiment 1.

[0109] like Figure 9 As shown, the computer terminal provided in this embodiment includes: at least one processor 101, and a memory 102 connected to at least one processor 101. This embodiment does not limit the specific connection medium between the processor 101 and the memory 102. Figure 9 The example shown is the connection between processor 101 and memory 102 via bus 100. Bus 100 is... Figure 9 The connections between other components are shown in bold lines and are for illustrative purposes only, not as limiting information. Bus 100 can be divided into address bus, data bus, control bus, etc., for ease of representation. Figure 9 The bus is represented by a single thick line, but this does not indicate that there is only one bus or one type of bus. Alternatively, the processor 101 may also be called a controller; there is no restriction on the name.

[0110] In this embodiment, the memory 102 stores instructions that can be executed by at least one processor 101. The at least one processor 101 can execute the aforementioned method by executing the instructions stored in the memory 102.

[0111] The processor 101 is the control center of the device. It can connect to various parts of the control device through various interfaces and lines. By running or executing instructions stored in memory 102 and calling data stored in memory 102, the processor can perform various functions and process data, thereby monitoring the device as a whole.

[0112] In one possible design, processor 101 may include one or more processing units. Processor 101 may integrate an application processor and a modem processor, wherein the application processor mainly handles the operating system, user interface, and applications, and the modem processor mainly handles wireless communication. It is understood that the modem processor may also not be integrated into processor 101. In some embodiments, processor 101 and memory 102 may be implemented on the same chip; in some embodiments, they may also be implemented on separate chips.

[0113] Processor 101 can be a general-purpose processor, such as a central processing unit (CPU), digital signal processor, application-specific integrated circuit, field-programmable gate array or other programmable logic device, discrete gate or transistor logic device, or discrete hardware component, capable of implementing or executing the methods, steps, and logic block diagrams disclosed in the embodiments. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the method for establishing the equivalent calculation model of the rail transmission line disclosed in Embodiment 1 can be directly manifested as being executed by a hardware processor, or executed by a combination of hardware and software modules in processor 101.

[0114] Memory 102, as a non-volatile computer-readable storage medium, can be used to store non-volatile software programs, non-volatile computer-executable programs, and modules. Memory 102 may include at least one type of storage medium, such as flash memory, hard disk, multimedia card, card-type memory, random access memory (RAM), static random access memory (SRAM), programmable read-only memory (PROM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), magnetic storage, magnetic disk, optical disk, etc. Memory 102 can be any other medium capable of carrying or storing desired program code in the form of instructions or data structures that can be accessed by a computer, but is not limited thereto. In this embodiment, memory 102 can also be a circuit or any other device capable of implementing storage functions for storing program instructions and / or data.

[0115] By designing and programming the processor 101, the code corresponding to the method for establishing the equivalent calculation model of the rail transmission line described in the foregoing embodiments can be embedded into the chip, thereby enabling the chip to execute the code during operation. Figure 1 The steps for establishing the equivalent calculation model of the rail transmission line are shown. How to design and program the processor 101 is a technique well-known to those skilled in the art and will not be elaborated upon here.

[0116] Example 3

[0117] This embodiment provides a computer-readable storage medium storing a computer program thereon. When the program is executed by a processor, it implements the steps of the method for establishing an equivalent calculation model of a rail transmission line as described in Embodiment 1.

[0118] The computer-readable storage medium may include flash memory, hard disk, multimedia card, card-type memory (e.g., SD or DX memory), random access memory (RAM), static random access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic memory, magnetic disk, optical disk, etc. In some embodiments, the storage medium may be an internal storage unit of a computer device, such as the hard disk or memory of the computer device. In other embodiments, the storage medium may also be an external storage device of the computer device, such as a plug-in hard disk, smart memory card, secure digital card, flash memory card, etc., provided on the computer device. Of course, the storage medium may include both internal storage units and external storage devices of the computer device. In this embodiment, the memory is typically used to store the operating system and various application software installed on the computer device. In addition, the memory can also be used to temporarily store various types of data that have been output or will be output.

[0119] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for establishing an equivalent calculation model of a rail transmission line, characterized in that, The lightning transient analysis method applied to non-standard I-beam steel rails includes the following steps: S1. Two virtual cylindrical current layers surrounding the rail conductor are set up to simplify the electromagnetic field of the lossy semi-infinite space where the rail is located into a system composed of the inner cylindrical current layer and the rail, and a system composed of the outer cylindrical current layer and the ground. The current amplitude applied to the two cylindrical current layers is equal to the rail current, and the directions of the inner and outer cylindrical currents are opposite, while the direction of the outer cylindrical current is the same as the rail current. The difference in the cylindrical radii of the two cylindrical current layers is within a set threshold, and the current density is uniformly distributed on the cylindrical surface, so that the electromagnetic fields generated by the two cylindrical current layers cancel each other out. S2. Calculate the impedance parameters of the system composed of the inner cylindrical surface current layer and the rail, the impedance parameters of the system composed of the outer cylindrical surface current layer and the earth, and the mutual impedance parameters of the rail respectively. S3. The effects of skin effect and magnetic saturation effect on rail impedance parameters are analyzed using finite element method (FEM) software. Based on the analysis results, the final rail frequency domain impedance parameter matrix used for modeling is obtained. The influence of magnetic saturation effect on the rail self-impedance parameters is ignored. Under the skin effect, the amplitude of the magnetic field and the current density inside the rail decrease exponentially with increasing distance from the conductor surface, as shown in the following formula: In the formula, y Indicates the depth from the surface of the conductor into the interior; Indicates depth Complex current density at the location, Represents the complex current density on the surface of a conductor; It is a natural constant; Indicates skin depth. Represents the imaginary unit. and These represent the decay constant and the phase constant, respectively. For skin depth The magnetic field amplitude decays to the level of the conductor surface. ; express Magnetic field strength at depth; The complex magnetic field strength at the surface of a conductor; skin depth The calculation formula is: In the formula, and These represent the electrical conductivity and magnetic permeability of the material, respectively. Indicates the frequency of the applied current; S4. Based on the rail frequency domain impedance parameter matrix, establish the time domain transmission line equation containing frequency-varying parameters.

2. The method for establishing an equivalent calculation model of a rail transmission line according to claim 1, characterized in that, In step S2, the calculation of the impedance parameters of the system consisting of the inner cylindrical surface current layer and the rail specifically includes: Obtaining the rail's self-impedance parameters: The electromagnetic field of the system consisting of the inner cylindrical surface current layer and the rail is solved using finite element software. Based on the power loss per unit length and the energy stored in the inductance, the resistance and inductance per unit length are calculated as follows: In the formula, Represents the resistance per unit length of the rail; This indicates the power loss per unit length of rail. Indicates the peak value of the excitation current; Represents the spatial current density distribution; Indicates the inductance per unit length of the rail; This represents the magnetic energy stored per unit length of rail. Indicates the distribution of magnetic flux density; Indicates the distribution of magnetic field strength; This indicates the cross-section of the rail. Represents an area element; Indicates the electrical conductivity of the rail; Obtaining the internal impedance parameters of the rail: Finite element method (FEM) software is used to calculate the power loss and stored magnetic field energy of the rail within the current layer of the inner cylindrical surface of a set radius, obtaining the resistance and inductance at different frequencies. The frequency-varying internal impedance parameters are then calculated using the following formula: In the formula, This represents the distributed impedance parameter of the rail. This represents the internal resistance of the rail that varies with the frequency of the excitation current. Represents the imaginary unit. Indicates angular frequency; Indicates the self-inductance of the rail; This represents the external equivalent inductance.

3. The method for establishing an equivalent calculation model of a rail transmission line according to claim 1, characterized in that, In step S2, calculating the impedance parameters of the system consisting of the outer cylindrical current layer and the ground specifically includes: The external impedance per unit length of rail is calculated using the following formula. : In the formula, Represents the imaginary unit. Indicates angular frequency; Indicates the permeability of free space; Indicates the height of the rail above the ground; Indicates the radius of the current layer on the outer cylindrical surface; This represents the complex propagation constant of the earth.

4. The method for establishing an equivalent calculation model of a rail transmission line according to claim 3, characterized in that, complex propagation constant of the earth The calculation formula is: In the formula, It represents the electrical conductivity of the earth; This represents the dielectric constant of the earth.

5. The method for establishing an equivalent calculation model of a rail transmission line according to claim 1, characterized in that, In step S2, the rail mutual impedance parameters are calculated using the generalized integral form of Carson ground impedance: In the formula, Indicates frequency as At that time, the steel rail and rails mutual impedance between Represents the imaginary unit. Indicates angular frequency; Indicates the permeability of free space; It is a natural constant; and These represent two adjacent rails. and Distance to the ground, ; Indicates the horizontal distance between two rails; Represents the integral variable; It represents the electrical conductivity of the earth.

6. The method for establishing an equivalent calculation model of a rail transmission line according to claim 1, characterized in that, In step S4, the expression formula for the time-domain transmission line equation containing frequency-varying parameters is as follows: In the formula, Represents partial derivatives; Represents a point in the transmission line x In time t The voltage; This represents the inductance matrix per unit length of a multi-conductor transmission line. Represents a point in the transmission line In time The current; Representing fractional impedance Z ( s freq The number of terms in a function fraction; and They represent Z ( s freq Residues and poles of partially fractional expressions; The symbol for convolution; This represents the capacitance matrix per unit length of a multi-conductor transmission line.

7. A computer terminal, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of establishing an equivalent calculation model for a rail transmission line as described in any one of claims 1 to 6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the method for establishing an equivalent calculation model of a rail transmission line as described in any one of claims 1 to 6.

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